A Useful Family of Stochastic Processesfor Modeling Shape Diffusions

One of the new area of research emerging in the field of statisticsis the shape analysis. Shape is defined as all the geometrical information ofan object whose location, scale and orientation is not of interest. Diffusionin shape analysis can be studied via either perturbation of the key coordinatesidentifying the initial object or random evolution of the shape itself.Reviewing the first case, we mainly consider the second case and particularlydefine a new family of diffusion processes. It can be used to model diffusionphenomena represented by shape evolution such as cell motion.